Type B plactic relations for $r$-domino tableaux

The recent work of Bonnafé et al. (2007) shows through two conjectures that $r$-domino tableaux have an important role in Kazhdan-Lusztig theory of type $B$ with unequal parameters. In this paper we provide plactic relations on signed permutations which determine whether given two signed permutation...

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Bibliographic Details
Published in:Discrete mathematics and theoretical computer science Vol. DMTCS Proceedings vol. AK,...; no. Proceedings; pp. 833 - 846
Main Author: Taşkın, Müge
Format: Journal Article Conference Proceeding
Language:English
Published: DMTCS 01.01.2009
Discrete Mathematics and Theoretical Computer Science
Discrete Mathematics & Theoretical Computer Science
Series:DMTCS Proceedings
Subjects:
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
[math.math-co] mathematics [math]/combinatorics [math.co]
Combinatorics
Computer Science
Discrete Mathematics
domino tableaux
insertion algorithm
Mathematics
plactic relations
domino tableaux
plactic relations
insertion algorithm
ISSN:1365-8050, 1462-7264, 1365-8050
Online Access:Get full text
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Summary:The recent work of Bonnafé et al. (2007) shows through two conjectures that $r$-domino tableaux have an important role in Kazhdan-Lusztig theory of type $B$ with unequal parameters. In this paper we provide plactic relations on signed permutations which determine whether given two signed permutations have the same insertion $r$-domino tableaux in Garfinkle's algorithm (1990). Moreover, we show that a particular extension of these relations can describe Garfinkle's equivalence relation on $r$-domino tableaux which is given through the notion of open cycles. With these results we enunciate the conjectures of Bonnafé et al. and provide necessary tool for their proofs.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.2700